I don't think examples of bad faith play, which is most of the
@overgeeked example above, really move the discussion along. What prevents the DM from being a jerk, in most cases is the either implied or formal social contract that governs pretty much any game table.
Agency and narrative control are not the same thing, and the example at hand is correctly identified as extraordinarily low agency compared to other games. I wasn't judging that state of affairs at all, obviously many people enjoy FRK games, just identifying the nature of one of the game elements.
Also, if you don't understand how adjudication frameworks add to player agency, perhaps stop and consider it for a moment. It is actually true, despite your protestations to the contrary.
@Malmuria - deciding by fiat that the goblins are immune to fire is not something that comes as a standard part of the DM tool kit, for 5E or any edition. Player knowledge of the rule enforces a certain amount of colouring inside the lines by the DM in terms of adjudication.
I'll bite.
I think you started by identifying the division correctly. But then ... not so much. So I will explain this in more detail.
Player agency (in other words, do players have
meaningful choices) is one thing.
Player authority is a different thing.
Let's break down player agency, first.
To have meaningful choice (beyond chargen, etc.), you usually need three things:
A. Player has control over the alter ego ("PC") decisions.
B. Decision must have consequences within the gameworld.
C. Player can reasonably anticipate consequences before making decisions.
A, B, C. That's a pretty standard way to look at it. Right? In a traditional RPG, such as D&D, this is achievable through the standard process of play.
1. The player declares the action.
2. The action will have consequences (that the DM will narrate) within the gameworld.
3. The player can reasonable anticipate the consequences of the decision.
Again, all of this requires the basic background of "Don't be a jerk" for the DM and the player - but it works. And it's the same with FKR, too!
When does this break? On the standard issues that people talk about in trad games when discussing player agency.
Player says, "I go west."
(DM has only planned one combat, and it was to the east, so moves it on the map to the east)
The action had no consequences- no agency.
The bard surrenders to the party.
Snarf says, "I kill the bard!"
The DM says, "No, you character wouldn't do that."
The player isn't allowed to declare their own action.
Fenris comes up with a great plan to bamboozle the shopkeeper.
The DM doesn't want that to happen, so decides that there is a spell there that is triggered by any bamboozling and prevents Fenris's plan.
The player could not reasonably anticipate the consequences of the decision.
Here, we have examples of the type that are CONSTANTLY DISCUSSED at enworld in terms of player agency- for someone to label these as "not player agency" is beyond silly.
That said, this is different that player authority. Player authority (the ability to narrate the fiction, or decide consequences) is also important to people, but to have a real discussion, you really need to separate it out from player agency.